Equatorial noise (EN) emissions are electromagnetic waves routinely observed in the inner magnetosphere within a few degrees from the geomagnetic equator. They propagate in the extraordinary mode nearly perpendicular to the ambient magnetic field, i.e., their frequencies are approximately limited by the lower hybrid frequency. Although they are usually continuous in time, about 5 percent of the events exhibit a clear quasiperiodic modulation of the wave intensity. We analyze in total 118 such EN events measured by the Cluster spacecraft. It is shown that more intense events typically have lower modulation periods. The fine harmonic structure identifiable when high resolution data are available allows us to estimate the radial distance of their source. We analyze in situ measured particle distribution functions and magnetic field pulsations in an attempt to determine the origin of the observed intensity variations. Finally, we use the data from the low altitude satellite DEMETER to demonstrate that these emissions can be observed at altitudes as low as 700 km, in particular during geomagnetically disturbed periods.